# Energy required to reach Escape Velocity

• mrxyz
In summary: However, I was asking specifically about the amount of fuel that would be required to reach escape velocity. I don't know how much the rocket / payload / fuel each weigh, and they are interrelated, so I'm hoping someone can help me figure that out.
mrxyz
Can anyone help me work out the energy required for a rocket powered craft to reach escape velocity.

What I'm looking to find is the amount of fuel (in any measurement) that will need to be burned simultaneously to achieve this for a craft carrying a payload of 5 to 10kg.

Any help/links to a source where I can work this out for myself would be much appreciated.

Thanks.

The closest you will probably find to a simple equation is this: http://exploration.grc.nasa.gov/education/rocket/rktpow.html

The problem is that you have to be able to estimate the full and empty weight and thrust. These aren't things generally just pulled out of the air -- they themselves can take thousands of hours of engineering work to figure out. However, you should be able to at least start by plugging the equation into a spreadsheet and playing with some test values. Perhaps take the specs for a real rocket and plug them in.

 The wiki page for the space shuttle SRBs has the takeoff, empty and propellant weights plus a thrust profile. Big rockets don't get much simpler than the SRB, so it is probably a good starting example (assume it can be launched autonomous).

Beyond that, the question gets extremely complicated to solve.

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Interesting use of the word 'simple' there lol.

I'm not that great with equations, is there a more English-friendly source?

I'm not sure what you mean by "English friendly source". The site was in English -- that's NASA. Here's the wiki page on it: http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

And by "simple" -- that equation requires nothing more than junior high school level algebra to manipulate. There is no math simpler than that unless we get rid of variables!

And just a friendly hint: the above was already given to you in your other thread, as well as an example of a similar project that succeeded. If you haven't already, it would be helpful for you to look into what it took for these amateurs just to reach the edge of space and fall back. http://en.wikipedia.org/wiki/Civilian_Space_eXploration_Team

 An additional approach that would be simpler (but less accurate of course) is to take the average thrust, time and beginning and final rocket mass (from the SRB wiki) and use Newton's laws of motion to compute the profile in a spreadsheet.

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russ_watters said:
I'm not sure what you mean by "English friendly source". The site was in English -- that's NASA. Here's the wiki page on it: http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

And by "simple" -- that equation requires nothing more than junior high school level algebra to manipulate. There is no math simpler than that unless we get rid of variables!

And just a friendly hint: the above was already given to you in your other thread, as well as an example of a similar project that succeeded. If you haven't already, it would be helpful for you to look into what it took for these amateurs just to reach the edge of space and fall back. http://en.wikipedia.org/wiki/Civilian_Space_eXploration_Team

 An additional approach that would be simpler (but less accurate of course) is to take the average thrust, time and beginning and final rocket mass (from the SRB wiki) and use Newton's laws of motion to compute the profile in a spreadsheet.

Thanks, yeah, I was meaning to look into the Tsiolkovsky rocket equation but got sidetracked by some other replies in that thread.

From a brief look into it - looks like it will take a lot of work for me to be able to fully 'get' these equations. I'm sure it can all be put into actual sentences with a better word to equation ratio and I hope someone has tried a near full textual explanation. Otherwise, I'll just have to get my maths up to par :P

If yourself or someone else could answer the specific question I asked about the amount of fuel required (even an approximation) who's better able to understand the equations at the current moment; I'd really appreciate that though.

mrxyz said:
... If yourself or someone else could answer the specific question I asked about the amount of fuel required (even an approximation) ...

Fuel requirement for WHAT. You still don't seem to get that you have to DESIGN THE ROCKET. There is no answer to your question until you have figured out how much the rocket / payload / fuel each weigh, and they are interrelated.

You really want for this to be simple, and it really ISN'T.

phinds said:
Fuel requirement for WHAT. You still don't seem to get that you have to DESIGN THE ROCKET. There is no answer to your question until you have figured out how much the rocket / payload / fuel each weigh, and they are interrelated.

You really want for this to be simple, and it really ISN'T.

I absolutely get that the rocket needs to be designed which is why I'm looking for a total and complete approximation. A small rocket but let's say the whole thing payload + the rocket's materials weigh 50kg.

Let's ASSUME for now the fuel will be weightless and adding it to the rocket will not bring it's total weight up at all. How much fuel needs to be burnt simultaneously for a 50kg rocket to reach 11.2km/s. I'm assuming the higher up it goes, the quicker it can pick up speed due to the decreased air friction, but correct me if I'm wrong here.

I understand what you're saying and even the type of propellant at each stage is important in this approximation, but let's hypothesise that each stage already has the best propellant inside it.

It would be a waste of time to not go through this hypothesizing process because if I was to get straight down the the planning and designing then weeks from now I may find out the whole thing is impossible to do. I'd rather discover that now if it's the case.

No, you can't assume the fuel is weightless. That's the heaviest part of the rocket.

There isn't much we can do to help someone who wants to be spoon-fed rocket science. You really need to make an attempt to learn what we have already given you. Please show us your attempt at one of the methods I gave you.

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Oh my goodness.

I'm willing to put in the work, but to work on a hopeless endeavour for months without knowing it's not going anywhere would be silly. The answer to my question will help me understand the feasibility.

Also, yes we can assume the fuel is weightless. I'm not planning to launch the rocket with fuel and pretending it's weightless - obviously not. It's more of a thought experiment.

mrxyz said:
... Yes we can assume the fuel is weightless.

no we can't

phinds said:
no we can't

fair enough.

Study the various topics here
http://exploration.grc.nasa.gov/education/rocket/shortr.html

and ultimately one wants to understand these in more detail
http://exploration.grc.nasa.gov/education/rocket/rktwtp.html
http://exploration.grc.nasa.gov/education/rocket/rktrflght.html

As others have indicated, there is a lot of work that goes into designing a rocket, and usually requires at least 6 years (and probably more like 8) of education, and a fair amount of study outside of a formal degree program.

One has to have fairly intimate knowledge of solid propellants and liquid propellants.

Perhaps one would be interested in Vanguard 1 (~1.4 kg) and the Explorer series of satellites.

http://en.wikipedia.org/wiki/Vanguard_1
http://en.wikipedia.org/wiki/Vanguard_rocket

Explorer 1 was about 14 kg.
http://en.wikipedia.org/wiki/Explorer_1

The first Explorer satellites were launched on Juno I rockets
http://en.wikipedia.org/wiki/Juno_I

http://history.nasa.gov/sputnik/expinfo.html

Even for 5 kgs to orbit, one will need several tons of rocket. This is not a trivial task, nor an endeavor for an individual.

One also needs clearance from US government, e.g., FAA and the military, to launch into orbit. There are lots of legal hurdles, e.g., a license to obtain and use solid rocket fuel in large quantities.

Also, note that the US and other nations have done small satellites already. It is unlikely that an individual would get permisson to launch a small 5-10 kg satellite into orbit. Space already has a lot of junk, and plenty of remote sensing systems in place.

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I will explore the links you've given in detail, and thank you very much for it.

One more point, I'm not in the US, in the UK actually. And from what I hear laws forbidding things like this aren't as strict.

I believe I can do this as impossible as it sounds. Who knows, as undoubtable as it seems due to my lack of knowledge of 1. mathematic equations and 2. propellants, most likely some other things.

My performance is always the best when I'm working on something I have a huge interest in, and is seemingly impossible.

If you never try you never succeed. So I think I'm up for this challenge!

mrxyz said:
I will explore the links you've given in detail, and thank you very much for it.

One more point, I'm not in the US, in the UK actually. And from what I hear laws forbidding things like this aren't as strict.

I believe I can do this as impossible as it sounds. Who knows, as undoubtable as it seems due to my lack of knowledge of 1. mathematic equations and 2. propellants, most likely some other things.

My performance is always the best when I'm working on something I have a huge interest in, and is seemingly impossible.

If you never try you never succeed. So I think I'm up for this challenge!

I admire your optimism and energy, but I don't think you have heard a thing we've been trying to tell you.

phinds said:
I admire your optimism and energy, but I don't think you have heard a thing we've been trying to tell you.

I think I know the things you're referring to, I'll say them again...

"It's impossible for one individual to carry out a project like this on a limited budget"
I don't think it's impossible, and if I later find out that there's a part of it which is impossible without a multi-million dollar budget then I'll come away having learned a lot about rocket science anyway, and no knowledge is ever wasted. Success or no success, I'll learn about a field I'm interested in.

"You don't currently have a detailed plan for it"
Every project at it's conception doesn't have a plan detailing all aspects of it. But all will be there in due time.

"You don't know enough about rocket science, propulsion systems, etc."

If there's still something you think I've missed please address it so I can clear that up too.

mrxyz said:
I will explore the links you've given in detail, and thank you very much for it.

One more point, I'm not in the US, in the UK actually. And from what I hear laws forbidding things like this aren't as strict.

I believe I can do this as impossible as it sounds. Who knows, as undoubtable as it seems due to my lack of knowledge of 1. mathematic equations and 2. propellants, most likely some other things.

My performance is always the best when I'm working on something I have a huge interest in, and is seemingly impossible.

If you never try you never succeed. So I think I'm up for this challenge!
I believe there are similar restrictions in the UK and EU.

http://www.europerocketry.com/index.php?id=309
If you expect your rocket to exceed 2000 feet in altitude, it is strongly recomended that you check with the CAA or obtain an air navigation map to ensure that your flight will not enter controlled airspace. For high power rocketry, high altitude flights or for large organised launch meetings it is advisable to contact the CAA to have a NOTAM (Notice To Airmen) issued.
. . . .
For High Power solid rocket motors, you need to obtain certification from the relevant authorities, which allows you to legally possesses the high power rocket motor propellant. This certification must then be produced to any UK High Power rocket motor propellant suppliers. The following facilities and documentation are required:

Storage Facilities
Registered Explosive Store Certificate
Explosive Certificate
Recipient Competent Authority (RCA) Transfer Document
. . . .
Rocket Motor Manufacture

Under the conditions of the 1875 Explosives Act, the 1883 Amendment, and later Prevention of Terrorism acts, it is an offence to manufacture your own solid fuel rocket motors, since these are classed as an explosive. This is also an issue for the Health and Safety Executive too. This act does not affect model rocketry enthusiasts who buy commercially available motors however, only those few people who want to construct their own solid fuel motors.
. . . .
Getting to orbit requires propulsion system well beyond 'model' or 'hobby' rockets! And one must check with the appropriate authorities.

The safety requirements for aerospace and nuclear systems are very stringent.

@mrxyz -- get the right education, get the appropriate government permits, and get the funding for your rocket launch. Once you have those, you may post here on the PF again about this project. Until then, this thread is closed, and you may not post here again about it until you achieve those 3 things.

## 1. What is escape velocity?

Escape velocity is the minimum speed an object needs to achieve in order to escape the gravitational pull of a larger object, such as a planet or moon.

## 2. How is escape velocity calculated?

Escape velocity is calculated using the equation v = √(2GM/R), where G is the gravitational constant, M is the mass of the larger object, and R is the distance between the center of the object and the object's surface.

## 3. What factors affect the energy required to reach escape velocity?

The energy required to reach escape velocity is affected by the mass and radius of the larger object, as well as the strength of its gravitational force.

## 4. Can escape velocity vary depending on the object's direction of travel?

Yes, the escape velocity can vary depending on the direction of the object's travel. If the object is traveling in the same direction as the rotation of the larger object, it will require less energy to escape. On the other hand, if the object is traveling in the opposite direction, it will require more energy to escape.

## 5. What is the practical application of understanding escape velocity?

Understanding escape velocity is important for space travel and exploration. It helps scientists and engineers determine the amount of energy and speed needed for spacecraft to leave the Earth's orbit and travel to other planets or moons in our solar system.

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